Using the spectral regression and Gaussian semiparametric methods of estimating the long-memory parameter, we test for fractional dynamic behavior in a number of important Japanese financial time series: spot exchange rates, forward exchange rates, stock prices, currency forward premia, Euroyen deposit rates, and the Euroyen term premium. Stochastic long memory is established as a feature of th...

We establish weak convergence of partial sums of tempered fractional time series (TFTS) to a stochastic process which we call a tempered Gaussian Hermite process (TGHP). We also introduce the Wiener integral with respect to TGHP, and establish weak convergence of weighted sums of TFTS to this Wiener integral.

Several signal processing tools are integrated into machine learning models for performance and computational cost improvements. Fourier transform (FT) its variants, which powerful spectral analysis, employed in the prediction of univariate time series by converting them to sequences domain be processed further recurrent neural networks (RNNs). This approach increases reduces training compared ...

We investigate compositional iteration of fractional order for transseries. For any large positive transseries T of exponentiality 0, there is a family T [s] indexed by real numbers s corresponding to iteration of order s. It is based on Abel’s Equation. We also investigate the question of whether there is a family T [s] all sharing a single support set. A subset of the transseries of exponenti...

Besides fractional Brownian motion most non-Gaussian fractional fields are obtained by integration of deterministic kernels with respect to a random infinitely divisible measure. In this paper, generalized shot noise series are used to obtain approximations of most of these fractional fields, including linear and harmonizable fractional stable fields. Almost sure and Lr-norm rates of convergenc...

The paper proposes a new approach to compute the impulse response of fractional order linear time invariant systems. By applying a general approach to decompose a Laplace transform into a Laurent like series, we obtain a power series that generalizes the Taylor and MacLaurin series. The algorithm is applied to the computation of the impulse response of causal linear fractional order systems. In...

In this article, fractional complex transform with optimal homotopy analysis method (OHAM) is used to obtain numerical and analytical solutions for the nonlinear time-space fractional Fornberg-Whitham. Fractional complex transform is proposed to convert time-space fractional Fornberg-Whitham equation to the nonlinear ordinary differential equations and then applied OHAM to the new obtained equa...

Recently much of the research has been dedicated to the application of fractional calculus in rheology. In this paper fractional-order spectra are presented for the complex viscoelastic materials, which mechanical analogy are constructed by fractional elements connected in series or parallel. Fractional-order spectra connect directly to the material’s constitutive relation with fractional deriv...